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Recent questions tagged quantifiers
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geeksforgeeks
Let S(x) be the predicate "x is a student",T(x) be the predicate "x is a teacher"and Q(x,y) be the predicate "x has asked y a question" where the domain consists of all people associated with the school. Use quantifiers to express the statement. "Some student ... ∀x∃y ( ( S(x) ∧ T(y) ) → Q(y,x) ) [ ¬P v Q = P→Q ] None of the options are matching .
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Jan 23
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Ashish Goyal
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Kenneth Rosen Edition 6th Exercise 1.4 Question 9f (Page No. 59)
Q) There is somebody whom no one loves L(x,y) : x loves y. Doubt: Does ∀x ∃y ~L(x,y) will be same as ∃x ∀y ~L(y,x) or both are different please give explaination
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Jan 10
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kd.....
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Kenneth Rosen Edition 6th Exercise 1.3 Question 53 (Page No. 50)
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Dec 16, 2018
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4
GATEBOOK2019DM11
Which of the following first order logic statement is equivalent to below statement? If anyone cheats, everyone suffers. $S_1 \forall x (\text{cheat}(x) \to \forall y \text{ suffer}(y))$ $S_2: \forall x\forall y (\text{cheat}(x) \to \text{ suffer}(y))$ Only $S1$ Only $S2$ Both $S1$ and $S2$ None
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Oct 28, 2018
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GATEBOOK2019DM13
Which of the following formulae is a formalization of the sentence: "There is a $\text{Computer}$ which is not used by any $\text{Student}$" $ \exists x (\text{Computer}(x) \wedge \forall y. (\sim \text{Student}(y) \wedge \sim \text{Uses}(y,x))) $ ... $ \exists x (\text{Computer} (x) \rightarrow \forall y . (\sim \text{Student} (y) \wedge \sim \text{Uses}(y,x)))$
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Oct 28, 2018
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Mathematical Logic
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GATEBOOK
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GATEBOOK2019DM14
Minesweeper is a singleplayer computer game invented by Robert Donner in 1989. A unary predicate mine is defined, where $\text{mine}(x)$ means that the cell $x$ ... $n$ mines in the game There are at most $n$ mines in the game None of the above
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Oct 28, 2018
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Mathematical Logic
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GATEBOOK
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GATEBOOK2019DM15
Which of the below first order logic formulae represent the sentence There is a student who is loved by every other student Here, $\text{Loves}(x,y)$ means $x$ loves $y$ ...
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Oct 28, 2018
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Mathematical Logic
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GATEBOOK2019DM111
Suppose that $P(x,y)$ means "x is a parent of y" and $M(x)$ means "x is a male". If $F(v,w)$ equals $M(v) \wedge \exists x \exists y (P(x,y) \wedge P(x,v) \wedge (y \neq v ) \wedge P(y,w)), $ the meaning of the expression $F(v,w)$ is $v$ is a brother of $w$ $v$ is an uncle of $w$ $v$ is a grandfather of $w$ $v$ is a nephew of $w$
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Oct 28, 2018
in
Mathematical Logic
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GATEBOOK
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63
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gb2019dm1
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2
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GATEBOOK2019DM112
Translate the following logic statement to English where, $A(x)$: $x$ is African, $F(x,y)$: x and y are friends. The universe for $x$ and $y$ is all the people in the world. $\forall x \exists y((A(x) \vee (F(x,y)))$ Every African has some African friend Every person who is not African has at least one friend Every person who has friend is not African None of these
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Oct 28, 2018
in
Mathematical Logic
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150
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2
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GATEBOOK2019DM113
Consider the following statement $ \exists x \: \exists y (\text{PARENT}(x, \text{Ramu}) \wedge \text{PARENT}(y, \text{Ramu}))$ where $\text{PARENT}(x,y)$ means $x$ is a parent of $y.$ Which of the following statement is true about ... order logic statement ? Ramu has at least one parent Ramu has at least two parents Ramu has at most one parent Ramu has at most two parents
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Oct 28, 2018
in
Mathematical Logic
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GATEBOOK2019DM116
Which of the following statements is not necessarily true ? $\forall x \: \forall y P(x,y) \Leftrightarrow \forall y \: \forall x P(x,y)$ $ \exists x \: \exists y P(x,y) \Leftrightarrow \exists y \: \exists x P(x,y)$ $\forall x \: \exists y P(x,y) \Rightarrow \exists y \: \forall x P(x,y) $ $ \exists y \:\forall x P(x,y) \Rightarrow \forall x \: \exists y P(x,y)$
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Oct 28, 2018
in
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GATEBOOK
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gb2019dm1
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+2
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1
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GATEBOOK2019DM119
Which of the following statements is FALSE $\exists x (P(x) \rightarrow Q(x)) \equiv \forall x P(x) \rightarrow \exists x Q(x) $ $\exists x (P(x) \vee Q(x)) \equiv \exists x P(x) \vee \exists x Q(x) $ $\forall x (P(x)\wedge Q(x)) \equiv \forall x P(x) \wedge \forall x Q(x) $ $\exists x (P(x)\wedge Q(x)) \equiv \exists x P(x) \wedge \exists x Q(x) $
asked
Oct 28, 2018
in
Mathematical Logic
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GATEBOOK
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15.3k
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93
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gb2019dm1
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13
Kenneth Rosen Edition 6th Exercise 1.4 Question 9 (Page No. 59)
Let L(x, y) be the statement x loves y, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of these statements. g) There is exactly one person whom everybody loves ... There is someone who loves no one besides himself or herself. How these are represented???? The answer given is:
asked
Jul 25, 2018
in
Mathematical Logic
by
Sandy Sharma
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1.3k
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26
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kennethrosen
discretemathematics
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Kenneth Rosen Edition 6th Exercise 1.4 Question 7 e,f (Page No. 58)
Let T (x, y) mean that student x likes cuisine y, where the domain for x consists of all students at your school and the domain for y consists of all cuisines. Express each of these statements by a simple English sentence. e ... have the same opinion (either they both like it or they both do not like it). How to reach the answers?
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Jul 24, 2018
in
Mathematical Logic
by
Sandy Sharma
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1.3k
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48
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kennethrosen
discretemathematics
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quantifiers
0
votes
2
answers
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UGCNETJuly2018II85
The equivalence of $\neg \: \exists \: x \: Q \: (x)$ is $\exists \: x \: \neg \: Q \: (x)$ $\forall \: x \: \neg \: Q \: (x)$ $\neg \: \exists \: x \: \neg \: Q \: (x)$ $\forall \: x \: Q \: (x)$
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Jul 13, 2018
in
Others
by
Pooja Khatri
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8.9k
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141
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ugcnetjuly2018ii
discretemathematics
quantifiers
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votes
1
answer
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Kenneth Rosen Edition 6th Exercise 1.3 Question 41b (Page No. 49)
Express each of these system specifications using predicates, quantifiers, and logical connectives b) Whenever there is an active alert, all queued messages are transmitted. There are two Solution to this AND Both seems correct to me . ... ) And the reason " we don't use implication with ∃x " Which leaves me in confusion.?
asked
Jul 6, 2018
in
Mathematical Logic
by
Sandy Sharma
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(
1.3k
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90
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kennethrosen
discretemathematics
mathematicallogic
quantifiers
0
votes
1
answer
17
Kenneth Rosen Edition 6th Exercise 1.3 Question 40c (Page No. 49)
Express each of these system specifications using predicates, quantifiers, and logical connectives. c) The file system cannot be backed up if there is a user currently logged on. I got this expression : ∃x(U(x)) > not F(x) ... the manual is: Which one is correct? If the manual is correct then why two variables x,y are required?
asked
Jul 6, 2018
in
Mathematical Logic
by
Sandy Sharma
Active
(
1.3k
points)

95
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kennethrosen
mathematicallogic
discretemathematics
quantifiers
0
votes
2
answers
18
Kenneth Rosen Edition 6th Exercise 1.4 Question 11f (Page No. 59)
Let S(x) be the predicate x is a student, F(x) the predicate x is a faculty member, and A(x, y) the predicate x has asked y a question, where the domain consists of all people associated with ... member, there exists some student who has not asked that faculty member a question. is both the above statements have same meaning?
asked
Jul 2, 2018
in
Mathematical Logic
by
Prince Sindhiya
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(
6.2k
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67
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kennethrosen
discretemathematics
quantifiers
0
votes
1
answer
19
Kenneth Rosen Edition 6th Exercise 1.3 Example 27 (Page No. 45)
Q)Consider these statements, of which the first three are and fourth is a valid conclusion. "All hummingbirds are richly colored." "No large birds live on honey." "Birds that do not live on honey are dull in color" "Hummingbirds are small." Express using quantifiers??
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Feb 18, 2018
in
Mathematical Logic
by
Lakshman Patel RJIT
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29.4k
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115
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propositionallogic
kennethrosen
discretemathematics
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+1
vote
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answers
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Universal Quantifier (Basics)
Which one of the expression of universal quantifier is ambiguous? For all For every all of for each for any for arbitrary
asked
Feb 9, 2018
in
Mathematical Logic
by
Mk Utkarsh
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34.2k
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128
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mathematicallogic
quantifiers
+1
vote
1
answer
21
First Order Logic
A = ∃x (P(x) ^ Q(x)). B = ∃x P(x) ^ ∃x Q(x). Which is correct? a) A => B b) B => A c) A <=> B d) None of These Please Explain.
asked
Oct 18, 2017
in
Mathematical Logic
by
nishant279
(
463
points)

211
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discretemathematics
mathematicallogic
firstorderlogic
propositionallogic
quantifiers
0
votes
0
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22
First Order Logic
A = ∃x(P(x)^Q(x)) B = ∃x P(x) ^ ∃x Q(x), which is correct? a) A <=> B b) A => B c) B => A d) None of These Please Explain.
asked
Oct 18, 2017
in
Mathematical Logic
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nishant279
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463
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131
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discretemathematics
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firstorderlogic
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quantifiers
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votes
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23
Rosen_Discrete_Mathematics_and_Its_Applications_7th_Edition/Pg.56/Section 1.4 :predicates and quantifiers/Q.43 and Q.44
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Aug 13, 2017
in
Mathematical Logic
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kmr_ndrsh
(
69
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118
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24
Kenneth Rosen Edition 6th Exercise 1.4 Question 35 (Page No. 61)
Find a common domain for the variables x, y, z, and w for which the statement $∀x∀y∀z∃w((w \neq x) ∧ (w \neq y) ∧ (w \neq z))$ is true and another common domain for these variables for which it is false.
asked
Jul 25, 2017
in
Mathematical Logic
by
Ali Jazib Mahmood
(
253
points)

82
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discretemathematics
kennethrosen
domain
mathematicallogic
quantifiers
+3
votes
1
answer
25
Discrete Maths: First Order Logic  Question in my mind based on question from Kenneth Rosen
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Jul 12, 2017
in
Mathematical Logic
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meghashyamc
(
377
points)

223
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quantifiers
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kennethrosen
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votes
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Kenneth Rosen Edition 6th Exercise 1.3 Question 41 c (Page No. 49)
Express using predicate,quantifies and connectives: The diagnostic monitor tracks status of all systems except main console
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Jun 9, 2017
in
Mathematical Logic
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rahul sharma 5
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81
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27
Quantifiers
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Jan 2, 2017
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Anup patel
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156
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quantifiers
+3
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2
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28
Logic
Everyone has exactly one best friend Are all three below same? Let B(x, y) to be the statement “y is the best friend of x" $ ∀x∃y(B(x, y) ∧ ∀z((z = y)→¬B(x, z))) $ $ ∀x ∃!y (B(x, y) $ $ ∀x ∃y (B(x, y) ∧ ∀z (B(x, z) → (y = z))) $
asked
Oct 18, 2016
in
Mathematical Logic
by
Shivam Chauhan
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9.1k
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297
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quantifiers
+4
votes
0
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29
Multiplicative inverse
Every real number except zero has a multiplicative inverse Are both the statements same? $ ∀x((x != 0) → ∃y(xy = 1)) $ $ ∀x ∃y ((x != 0) → (xy = 1)) $
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Oct 18, 2016
in
Mathematical Logic
by
Shivam Chauhan
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9.1k
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209
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quantifiers
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1
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30
Kenneth Rosen Edition 6th Exercise 1.3 Example 17 (Page No. 38)
The restriction of a universal quantification is the same as the universal quantification of a conditional statement. For instance, ∀x < 0 (x2 > 0) is another way of expressing ∀x(x < 0 ... whereas existential quantification is same as existential quantification of a conjunction? Please provide proper details. Thank You.
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Jul 1, 2016
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Mathematical Logic
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Navneet Srivastava
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137
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147
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